Answer:
4:5
Step-by-step explanation:
half of 16 is 8, and half of 8 is 4
and half of 20 is 10, and half of 10 is 5
hope i helped man
Answer:
Step-by-step explanation:
Sum of angle in a triangle = 180°
<A+<B+<C = 180
Given <B = 50°
Substituting into the formula
<A+50+<C = 180
<A+<C = 180-50
<A+<C = 130°
Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°
The possible values of <A and <C that will be acute and give a sum of 130° are;
∠A= 58° and ∠C= 72°
∠A= 80° and ∠C= 50°
∠A= 60° and ∠C= 70°
You can see that all the Angles are less than 90° and their sum is 130°
Answer:
We want to find:
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D)
Here we can use Stirling's approximation, which says that for large values of n, we get:

Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7B%5Csqrt%7B2%2A%5Cpi%2An%7D%20%2A%28%5Cfrac%7Bn%7D%7Be%7D%20%29%5En%7D%20%7D%7Bn%7D%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bn%7D%7Be%2An%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D)
Now we can just simplify this, so we get:
![\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Be%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D%20%5C%5C)
And we can rewrite it as:

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:

Answer:
1.5 times.
Step-by-step explanation:
6.75 / 4.5 = 1.5.
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
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Edit: Thanks to Chegsnut36 for calculation correction